Descriptive Statistics

Overview

This gem adds methods to the Enumerable module to allow easy calculation of basic descriptive statistics of Numeric sample data in collections that have included Enumerable such as Array, Hash, Set, and Range. The statistics that can be calculated are:

• Number
• Sum
• Mean
• Median
• Mode
• Variance
• Standard Deviation
• Percentile
• Percentile Rank
• Descriptive Statistics
• Quartiles

When requiring DescriptiveStatistics, the Enumerable module is monkey patched so that the statistical methods are available on any instance of a class that has included Enumerable. For example with an Array:

require 'descriptive_statistics'
data = [2,6,9,3,5,1,8,3,6,9,2]
# => [2, 6, 9, 3, 5, 1, 8, 3, 6, 9, 2]
data.number
# => 11.0
data.sum
# => 54.0
data.mean
# => 4.909090909090909
data.median
# => 5.0
data.variance
# => 7.7190082644628095
data.standard_deviation
# => 2.778310325442932
data.percentile(30)
# => 3.0
data.percentile(70)
# => 6.0
data.percentile_rank(8)
# => 81.81818181818183
data.mode
# => 2
data.range
# => 8
data.descriptive_statistics
# => {:number=>11.0,
  :sum=>54,
  :variance=>7.7190082644628095,
  :standard_deviation=>2.778310325442932,
  :min=>1,
  :max=>9,
  :mean=>4.909090909090909,
  :mode=>2,
  :median=>5.0,
  :range=>8.0,
  :q1=>2.5,
  :q2=>5.0,
  :q3=>7.0}

and with other types of objects:

require 'set'
require 'descriptive_statistics'
{:a=>1, :b=>2, :c=>3, :d=>4, :e=>5}.mean #Hash
# => 3.0
Set.new([1,2,3,4,5]).mean #Set
# => 3.0
(1..5).mean #Range
# => 3.0

including instances of your own classes, when an each method is provided that creates an Enumerator over the sample data to be operated upon:

class Foo
  include Enumerable
  attr_accessor :bar, :baz, :bat

  def each
    [@bar, @baz, @bat].each
  end
end

foo = Foo.new
foo.bar = 1
foo.baz = 2
foo.bat = 3
foo.mean
# => 2.0

or:

class Foo
  include Enumerable
  attr_accessor :bar, :baz, :bat

  def each
    Enumerator.new do |y|
      y << @bar
      y << @baz
      y << @bat
    end
  end
end

foo = Foo.new
foo.bar = 1
foo.baz = 2
foo.bat = 3
foo.mean
# => 2.0

and even Structs:

Scores = Struct.new(:sally, :john, :peter)
bowling = Scores.new
bowling.sally = 203
bowling.john = 134
bowling.peter = 233
bowling.mean
# => 190.0

All methods optionally take blocks that operate on object values. For example:

require 'descriptive_statistics'
LineItem = Struct.new(:price, :quantity)
cart = [ LineItem.new(2.50, 2), LineItem.new(5.10, 9), LineItem.new(4.00, 5) ]
total_items = cart.sum(&:quantity)
# => 16
total_price = cart.sum{ |i| i.price * i.quantity }
# => 70.9

Note that you can extend DescriptiveStatistics on individual objects by requiring DescriptiveStatistics safely, thus avoiding the monkey patch. For example:

require 'descriptive_statistics/safe'
data = [2,6,9,3,5,1,8,3,6,9,2]
# => [2, 6, 9, 3, 5, 1, 8, 3, 6, 9, 2]
data.extend(DescriptiveStatistics)
# => [2, 6, 9, 3, 5, 1, 8, 3, 6, 9, 2]
data.number
# => 11.0
data.sum
# => 54

Or, if you prefer leaving your collection pristine, you can create a Stats object that references your collection:

require 'descriptive_statistics/safe'
data = [1, 2, 3, 4, 5, 1]
# => [1, 2, 3, 4, 5, 1]
stats = DescriptiveStatistics::Stats.new(data)
# => [1, 2, 3, 4, 5, 1]
stats.class
# => DescriptiveStatistics::Stats
stats.mean
# => 2.6666666666666665
stats.median
# => 2.5
stats.mode
# => 1
data << 2
# => [1, 2, 3, 4, 5, 1, 2]
data << 2
# => [1, 2, 3, 4, 5, 1, 2, 2]
stats.mode
# => 2

Or you call the statistical methods directly:

require 'descriptive_statistics/safe'
# => true
DescriptiveStatistics.mean([1,2,3,4,5])
# => 3.0
DescriptiveStatistics.mode([1,2,3,4,5])
# => 1
DescriptiveStatistics.variance([1,2,3,4,5])
# => 2.0

Or you can use Refinements (available in Ruby >= 2.1) to augment any class that mixes in the Enumerable module. Refinements are lexically scoped and so the statistical methods will only be available in the file where they are used. Note that the lexical scope can be limited to a Class or Module, but only applies to code in that file. This approach provides a great deal of protection against introducing conflicting modifications to Enumerable while retaining the convenience of the monkey patch approach.

require 'descriptive_statistics/refinement'

class SomeServiceClass
  using DescriptiveStatistics::Refinement.new(Array)

  def self.calculate_something(array)
    array.standard_deviation
  end
end

[1,2,3].standard_deviation
# => NoMethodError: undefined method `standard_deviation' for [1, 2, 3]:Array

SomeServiceClass.calculate_something([1,2,3])
#=> 0.816496580927726

Ruby on Rails

To use DescriptiveStatistics with Ruby on Rails add DescriptiveStatistics to your Gemfile, requiring the safe extension.

source 'https://rubygems.org'

gem 'rails', '4.1.7'
gem 'descriptive_statistics', '~> 2.4.0', :require => 'descriptive_statistics/safe'

Then after a bundle install, you can extend DescriptiveStatistics on an individual collection and call the statistical methods as needed.

users = User.all.extend(DescriptiveStatistics)
mean_age = users.mean(&:age) # => 19.428571428571427
mean_age_in_dog_years = users.mean { |user| user.age / 7.0 } # => 2.7755102040816326

Notes

• All methods return a Float object except for mode, which will return a Numeric object from the collection. mode will always return nil for empty collections.
• All methods return nil when the collection is empty, except for number, which returns 0.0. This is a different behavior than ActiveSupport's Enumerable monkey patch of sum, which by deafult returns the Fixnum 0 for empty collections. You can change this behavior by specifying the default value returned for empty collections all at once:

require 'descriptive_statistics' [].mean

=> nil

[].sum

=> nil

DescriptiveStatistics.empty_collection_default_value = 0.0

=> 0.0

[].mean

=> 0.0

[].sum

=> 0.0

or one at a time:
```ruby
require 'descriptive_statistics'
[].mean
# => nil
[].sum
# => nil
DescriptiveStatistics.sum_empty_collection_default_value = 0.0
# => 0.0
[].mean
# => nil
[].sum
# => 0.0
DescriptiveStatistics.mean_empty_collection_default_value = 0.0
# => 0.0
[].mean
# => 0.0
[].sum
# => 0.0

• The scope of this gem covers Descriptive Statistics and not Inferential Statistics. From wikipedia:

  Descriptive statistics is the discipline of quantitatively describing the main features of a collection of information, or the quantitative description itself. Descriptive statistics are distinguished from inferential statistics, in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.

  Thus, all statistics calculated herein describe only the values in the collection. Where this makes a practical difference is in the calculation of variance (and thus the standard deviation which is derived from variance). We use the population variance to calculate the variance of the values in the collection. If the values in your collection represent a sampling from a larger population of values, and your goal is to estimate the population variance from your sample, you should use the inferential statistic, sample variance. However, the calculation of the sample variance is outside the scope of this gem's functionality.

Ports

Javascript

Python

Go

Elixir

Clojure

License

Copyright (c) 2010-2014 Derrick Parkhurst (derrick.parkhurst@gmail.com), Gregory Brown (gregory.t.brown@gmail.com), Daniel Farrell (danielfarrell76@gmail.com), Graham Malmgren, Guy Shechter, Charlie Egan (charlieegan3@googlemail.com)

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.